Report Title: Energy stability and error analysis of a maximum bound principle preserving scheme for the dynamical Ginzburg-Landau equations of Superconductivity

Reporter：Professor Qiao Zhonghua (Hong Kong Polytechnic University)

Report time：April 10, 2023 10:30-11:30

Report place：Huixing Building Institute of Fintech Room 4 Lecture Hall　

Content Overview：

We focus on numerical study of the dynamical Ginzburg-Landau equations under the temporal gauge, and propose a decoupled numerical scheme based on the finite element method. For the variable A, the second type Nedelec element is employed for the space discretization and the backward Euler is applied for the time discretization where the nonlinear term is treated explicitly. For the order parameter, the first order exponential time differencing method is employed with the linear operator generated by the linear element method with lumping. The proposed numerical scheme is proved to preserve the discrete maximum bound principle for the order parameter and admit an unconditional energy decay property. An optimal error estimate is also given for the scheme which is verified by the numerical examples.